Flutter stability analysis of an elastically supported flexible foil. Application to the energy harvesting of a fully-passive flexible flapping-foil of small amplitude

Abstract

The aerodynamic forces on an oscillating flexible foil are used to study the flutter instability when the flexible foil is elastically mounted to translational and torsional springs and dampers at an arbitrary pivot axis. The present linear theory, valid for small amplitudes of the heaving, pitching and flexural deflection motions, and therefore valid for sufficiently large stiffness ratios, characterizes analytically the onset of the flutter instability and the corresponding leading frequency in terms of the flow velocity and all the structural parameters of the system. The analysis may serve to guide the search for the parametric ranges of energy extraction by a fully-passive flexible flapping-foil hydrokinetic turbine, including the effect of some relevant nondimensional parameters which have not been considered before. The results for the rigid-foil case are validated with recent numerical simulations for a fully-passive flapping-foil turbine. As the stiffness of the foil decreases, the coupled-mode flutter instability of the elastically supported rigid foil may weaken and disappear, or become enhanced, depending on the remaining parameters, most particularly on the location of the centre of mass in relation to the pivot point, whose dependence is investigated for specific values of the rest of the nondimensional parameters.